Caesium standard

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Caesium_standard 

A caesium atomic fountain used as part of an atomic clock

The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

Caesium atomic clocks are one of the most accurate time and frequency standards, and serve as the primary standard for the definition of the second in the International System of Units (SI), the modern metric system. By definition, radiation produced by the transition between the two hyperfine ground states of caesium-133 (in the absence of external influences such as the Earth's magnetic field) has a frequency, Δν_Cs, of exactly 9192631770 Hz. That value was chosen so that the caesium second equaled, to the limit of measuring ability in 1960 when it was adopted, the existing standard ephemeris second based on the Earth's orbit around the Sun. Because no other measurement involving time had been as precise, the effect of the change was less than the experimental uncertainty of all existing measurements.

While the second is the only base unit to be explicitly defined in terms of the caesium standard, the majority of SI units have definitions that mention either the second, or other units defined using the second. Consequently, every base unit except the mole and every named derived unit except the coulomb, gray, sievert, radian, and steradian have values that are implicitly at least partially defined by the properties of the caesium-133 hyperfine transition radiation. And of these, all but the mole, the coulomb, and the dimensionless radian and steradian are implicitly defined by the general properties of electromagnetic radiation.

Technical details

The official definition of the second was first given by the BIPM at the 13th General Conference on Weights and Measures in 1967 as: "The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." At its 1997 meeting the BIPM added to the previous definition the following specification: "This definition refers to a caesium atom at rest at a temperature of 0 K."

The BIPM restated this definition in its 26th conference (2018), "The second is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s⁻¹."

The meaning of the preceding definition is as follows. The caesium atom has a ground state electron state with configuration [Xe] 6s¹ and, consequently, atomic term symbol ²S_1/2. This means that there is one unpaired electron and the total electron spin of the atom is 1/2. Moreover, the nucleus of caesium-133 has a nuclear spin equal to 7/2. The simultaneous presence of electron spin and nuclear spin leads, by a mechanism called hyperfine interaction, to a (small) splitting of all energy levels into two sub-levels. One of the sub-levels corresponds to the electron and nuclear spin being parallel (i.e., pointing in the same direction), leading to a total spin F equal to F = 7/2 + 1/2 = 4; the other sub-level corresponds to anti-parallel electron and nuclear spin (i.e., pointing in opposite directions), leading to a total spin F = 7/2 − 1/2 = 3. In the caesium atom it so happens that the sub-level lowest in energy is the one with F = 3, while the F = 4 sub-level lies energetically slightly above. When the atom is irradiated with electromagnetic radiation having an energy corresponding to the energetic difference between the two sub-levels the radiation is absorbed and the atom is excited, going from the F = 3 sub-level to the F = 4 one. After some time the atom will re-emit the radiation and return to its F = 3 ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly 9.19263177 GHz, corresponding to a wavelength of about 3.26 cm and therefore belonging to the microwave range.

Note that a common confusion involves the conversion from angular frequency (${\displaystyle \omega }$) to frequency (${\displaystyle f}$), or vice versa. Angular frequencies are conventionally given as s⁻¹ in scientific literature, but here the units implicitly mean radians per second. In contrast, the unit Hz should be interpreted as cycles per second. The conversion formula is ${\displaystyle \omega =2\pi f}$, which implies that 1 Hz corresponds to an angular frequency of approximately 6.28 radians per second (or 6.28 s⁻¹ where radians is omitted for brevity by convention).

Parameters and significance in the second and other SI units

Suppose the caesium standard has the parameters:

• Velocity: c
• Energy/frequency: h
• Time period: Δt_Cs
• Frequency: Δν_Cs
• Wavelength: Δλ_Cs
• Photon energy: ΔE_Cs
• Photon mass equivalent: ΔM_Cs

Time and frequency

The first set of units defined using the caesium standard were those relating to time, with the second being defined in 1967 as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom" meaning that:

• 1 second, s, = 9,192,631,770 Δt_Cs
• 1 hertz, Hz, = 1/s = ⁠Δν_Cs/9,192,631,770⁠
• 1 becquerel, Bq, = 1 nuclear decay/s = ⁠1/9,192,631,770⁠ nuclear decays/Δt_Cs

This also linked the definitions of the derived units relating to force and energy (see below) and of the ampere, whose definition at the time made reference to the newton, to the caesium standard. Before 1967 the SI units of time and frequency were defined using the tropical year and before 1960 by the length of the mean solar day

Length

In 1983, the meter was, indirectly, defined in terms of the caesium standard with the formal definition "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This implied:

• 1 metre, m, = ⁠c s/299,792,458⁠ = ⁠9,192,631,770/299,792,458⁠ c Δt_Cs = ⁠9,192,631,770/299,792,458⁠ Δλ_Cs
• 1 radian, rad, = 1 m/m = Δλ_Cs/Δλ_Cs = 1 (dimensionless unit of angle)
• 1 steradian, sr, = 1 m²/m² = Δλ_Cs²/Δλ_Cs² = 1 (dimensionless unit of solid angle)

Between 1960 and 1983, the metre had been defined by the wavelength of a different transition frequency associated with the krypton-86 atom. This had a much higher frequency and shorter wavelength than the caesium standard, falling inside the visible spectrum. The first definition, used between 1889 and 1960, was by the international prototype meter.

Mass, energy, and force

Following the 2019 revision of the SI, electromagnetic radiation, in general, was explicitly defined to have the exact parameters:

• c = 299,792,458 m/s
• h = 6.62607015×10⁻³⁴ J s

The caesium-133 hyperfine transition radiation was explicitly defined to have frequency:

• Δν_Cs = 9,192,631,770 Hz

Though the above values for c and Δν_Cs were already obviously implicit in the definitions of the metre and second. Together they imply:

• Δt_Cs = ⁠1/Δν_Cs⁠ = ⁠s/9,192,631,770⁠
• Δλ_Cs = c Δt_Cs = ⁠299,792,458/9,192,631,770⁠ m
• ΔE_Cs = h Δν_Cs = 9,192,631,770 Hz × 6.62607015×10⁻³⁴ J s = 6.09110229711386655×10⁻²⁴ J
• ΔM_Cs = ⁠ΔE_Cs/c²⁠ = ⁠6.09110229711386655×10⁻²⁴ J/89,875,517,873,681,764 m²/s²⁠ = ⁠6.09110229711386655/8.9875517873681764×10⁴⁰⁠ kg

Notably, the wavelength has a fairly human-sized value of about 3.26 centimetres and the photon energy is surprisingly close to the average molecular kinetic energy per degree of freedom per kelvin. From these it follows that:

• 1 kilogram, kg, = ⁠8.9875517873681764×10⁴⁰/6.09110229711386655⁠ ΔM_Cs
• 1 joule, J, = ⁠10²⁴/6.09110229711386655⁠ ΔE_Cs
• 1 watt, W, = 1 J/s = ⁠10¹⁴/5.59932604907689089550702935⁠ ΔE_Cs Δν_Cs
• 1 newton, N, = 1 J/m = ⁠2.99792458×10²²/5.59932604907689089550702935⁠ ΔE_Cs/Δλ_Cs
• 1 pascal, Pa, = 1 N/m² = ⁠2.6944002417373989539335912×10¹⁹/4.73168129737820913189287698892486811451620615⁠ ΔE_Cs/Δλ_Cs³
• 1 gray, Gy, = 1 J/kg = ⁠1/89,875,517,873,681,764⁠ ΔE_Cs/ΔM_Cs = ⁠c²/89,875,517,873,681,764⁠
• 1 sievert, Sv, = the ionizing radiation dose equivalent to 1 gray of gamma rays

Prior to the revision, between 1889 and 2019, the family of metric (and later SI) units relating to mass, force, and energy were somewhat notoriously defined by the mass of the International Prototype of the Kilogram (IPK), a specific object stored at the headquarters of the International Bureau of Weights and Measures in Paris, meaning that any change to the mass of that object would have resulted in a change to the size of the kilogram and of the many other units whose value at the time depended on that of the kilogram.

Temperature

From 1954 to 2019, the SI temperature scales were defined using the triple point of water and absolute zero. The 2019 revision replaced these with an assigned value for the Boltzmann constant, k, of 1.380649×10⁻²³ J/K, implying:

• 1 kelvin, K, = 1.380649×10⁻²³ J/2 per degree of freedom = ⁠1.380649×10⁻²³ × 10²⁴/2/6.09110229711386655⁠ ΔE_Cs per degree of freedom = ⁠1.380649/1.21822045942277331⁠ ΔE_Cs per degree of freedom
• Temperature in degrees Celsius, °C, = temperature in kelvins − 273.15 = ⁠1.21822045942277331 × kinetic energy per degree of freedom − 377.12427435 ΔE_Cs/1.380649 ΔE_Cs⁠

Amount of substance

The mole is an extremely large number of "elementary entities" (i.e. atoms, molecules, ions, etc). From 1969 to 2019, this number was 0.012 × the mass ratio between the IPK and a carbon 12 atom. The 2019 revision simplified this by assigning the Avogadro constant the exact value 6.02214076×10²³ elementary entities per mole, thus, uniquely among the base units, the mole maintained its independence from the caesium standard:

• 1 mole, mol, = 6.02214076×10²³ elementary entities
• 1 katal, kat, = 1 mol/s = ⁠6.02214076×10¹⁴/9.19263177⁠ elementary entities/Δt_Cs

Electromagnetic units

Prior to the revision, the ampere was defined as the current needed to produce a force between 2 parallel wires 1 m apart of 0.2 μN per meter. The 2019 revision replaced this definition by giving the charge on the electron, e, the exact value 1.602176634×10⁻¹⁹ coulombs. Somewhat incongruously, the coulomb is still considered a derived unit and the ampere a base unit, rather than vice versa. In any case, this convention entailed the following exact relationships between the SI electromagnetic units, elementary charge, and the caesium-133 hyperfine transition radiation:

• 1 coulomb, C, = ⁠10¹⁹/1.602176634⁠ e
• 1 ampere, or amp, A, = 1 C/s = ⁠10⁹/1.472821982686006218⁠ e Δν_Cs
• 1 volt, V, = 1 J/C = ⁠1.602176634×10⁵/6.09110229711386655⁠ ΔE_Cs/e
• 1 farad, F, = 1 C/V = ⁠6.09110229711386655×10¹⁴/2.566969966535569956⁠ e²/ΔE_Cs
• 1 ohm, Ω, = 1 V/A = ⁠2.359720966701071721258310212×10⁻⁴/6.09110229711386655⁠ ΔE_Cs/Δν_Cs e² = ⁠2.359720966701071721258310212×10⁻⁴/6.09110229711386655⁠ h/e²
• 1 siemens, S, = 1/Ω = ⁠6.09110229711386655×10⁴/2.359720966701071721258310212⁠ e²/h
• 1 weber, Wb, = 1 V s = ⁠1.602176634×10¹⁵/6.62607015⁠ ΔE_Cs Δt_Cs/e = ⁠1.602176634×10¹⁵/6.62607015⁠ h/e
• 1 tesla, T, = 1 Wb/m² = ⁠1.43996454705862285832702376×10¹²/5.59932604907689089550702935⁠ ΔE_Cs Δt_Cs/e Δλ_Cs² = ⁠1.43996454705862285832702376×10¹²/5.59932604907689089550702935⁠ E/e c Δλ_Cs
• 1 henry, H, = Ω s = ⁠2.359720966701071721258310212×10⁶/6.62607015⁠ h Δt_Cs/e²

Optical units

From 1967 to 1979 the SI optical units, lumen, lux, and candela are defined using the incandescent glow of platinum at its melting point. After 1979, the candela was defined as the luminous intensity of a monochromatic visible light source of frequency 540 THz (i.e ⁠6000/1.02140353⁠ that of the caesium standard) and radiant intensity ⁠1/683⁠ watts per steradian. This linked the definition of the candela to the caesium standard and, until 2019, to the IPK. Unlike the units relating to mass, energy, temperature, amount of substance, and electromagnetism, the optical units were not massively redefined in 2019, though they were indirectly affected since their values depend on that of the watt, and hence of the kilogram. The frequency used to define the optical units has the parameters:

• Frequency: 540 THz
• Time period: ⁠50/27⁠ fs
• Wavelength: ⁠14.9896229/27⁠ μm
• Photon energy: 5.4×10¹⁴ Hz × 6.62607015×10⁻³⁴ J s = 3.578077881×10⁻¹⁹ J
• luminous efficacy, K_CD, = 683 lm/W
• luminous energy per photon, ${\displaystyle Q_{\mathrm{v}}}$, = 3.578077881×10⁻¹⁹ J × 683 lm/W = 2.443827192723×10⁻¹⁶ lm s

This implies:

• 1 lumen, lm, = ⁠10⁶/2.246520349221536260971⁠ ${\displaystyle Q_{\mathrm{v}}}$ Δν_Cs
• 1 candela, cd, = 1 lm/sr = ⁠10⁶/2.246520349221536260971⁠ ${\displaystyle Q_{\mathrm{v}}}$ Δν_Cs/sr
• 1 lux, lx, = 1 lm/m² = ⁠8.9875517873681764×10²/1.898410313566852566340456048807087002459⁠ ${\displaystyle Q_{\mathrm{v}}}$ Δν_Cs/Δλ_Cs²

Summary

The parameters of the caesium-133 hyperfine transition radiation expressed exactly in SI units are:

• Frequency = 9,192,631,770 Hz
• Time period = ⁠1/9,192,631,770⁠ s
• Wavelength = ⁠299,792,458/9,192,631,770⁠ m
• Photon energy = 6.09110229711386655×10⁻²⁴ J
• Photon mass equivalent = ⁠6.09110229711386655×10⁻⁴⁰/8.9875517873681764⁠ kg

If the seven base units of the SI are expressed explicitly in terms of the SI defining constants, they are:

• 1 second = ⁠9,192,631,770/Δν_Cs⁠
• 1 metre = ⁠9,192,631,770/299,792,458⁠ c/Δν_Cs
• 1 kilogram = ⁠8.9875517873681764×10⁴⁰/6.09110229711386655⁠ h Δν_Cs/c²
• 1 ampere = ⁠10⁹/1.472821982686006218⁠ e Δν_Cs
• 1 kelvin = ⁠13.80649/6.09110229711386655⁠ h Δν_Cs/k
• 1 mole = 6.02214076×10²³ elementary entities
• 1 candela = ⁠10¹¹/3.82433969151951648163130104605⁠ h Δν_Cs² K_CD/sr

Ultimately, 6 of the 7 base units (all but the dimensionless mole) notably have values that depend on that of Δν_Cs, which appears far more often than any of the other defining constants. However, the derived unit of one coulomb, which is an ampere-second, is a dimensionful unit defined purely in terms of the elementary charge and hence is independent of Δν_Cs.

Paraphyly

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Paraphyly 

In this phylogenetic tree, the green group is paraphyletic; it is composed of a common ancestor (the lowest green vertical stem) and some of its descendants, but it excludes the blue group (a monophyletic group) which diverged from the green group.

Paraphyly is a taxonomic term describing a grouping that consists of the grouping's last common ancestor and some but not all of its descendant lineages. The grouping is said to be paraphyletic with respect to the excluded subgroups. In contrast, a monophyletic grouping (a clade) includes a common ancestor and all of its descendants.

The terms are commonly used in phylogenetics (a subfield of biology) and in the tree model of historical linguistics. Paraphyletic groups are identified by a combination of synapomorphies and symplesiomorphies. If many subgroups are missing from the named group, it is said to be polyparaphyletic.

The term received currency during the debates of the 1960s and 1970s accompanying the rise of cladistics, having been coined by zoologist Willi Hennig to apply to well-known taxa like Reptilia (reptiles), which is paraphyletic with respect to birds. Reptilia contains the last common ancestor of reptiles and all descendants of that ancestor except for birds. Other commonly recognized paraphyletic groups include fish, monkeys, lizards,, wasps, and crustaceans.

Etymology

The term paraphyly, or paraphyletic, derives from the two Ancient Greek words παρά (pará), meaning "beside, near", and φῦλον (phûlon), meaning "genus, species", and refers to the situation in which one or several monophyletic subgroups of organisms (e.g., genera, species) are left apart from all other descendants of a unique common ancestor.

Conversely, the term monophyly, or monophyletic, builds on the Ancient Greek prefix μόνος (mónos), meaning "alone, only, unique", and refers to the fact that a monophyletic group includes organisms consisting of all the descendants of a unique common ancestor.

By comparison, the term polyphyly, or polyphyletic, uses the Ancient Greek prefix πολύς (polús), meaning "many, a lot of". and refers to the fact that a polyphyletic group includes organisms arising from multiple ancestral sources.

Phylogenetics

Cladogram of the primates, showing a monophyly (the simians, in yellow), a paraphyly (the prosimians, in blue, including the red patch), and a polyphyly (the night-active primates, the lorises and the tarsiers, in red). "Monkeys" too are paraphyletic if apes and humans are excluded.

In cladistics

Further information: Cladistics

Groups that include all the descendants of a common ancestor are said to be monophyletic. A paraphyletic group is a monophyletic group from which one or more subsidiary clades (monophyletic groups) are excluded to form a separate group. Philosopher of science Marc Ereshefsky has argued that paraphyletic taxa are the result of anagenesis in the excluded group or groups. A cladistic approach normally does not grant paraphyletic assemblages the status of "groups", nor does it reify them with explanations, as in cladistics they are not seen as the actual products of evolutionary events.

A group whose identifying features evolved convergently in two or more lineages is polyphyletic (Greek πολύς [polys], "many"). More broadly, any taxon that is not paraphyletic or monophyletic can be called polyphyletic. Empirically, the distinction between polyphyletic groups and paraphyletic groups is rather arbitrary, since the character states of common ancestors are inferences, not observations.

These terms were developed during the debates of the 1960s and 1970s accompanying the rise of cladistics.

Paraphyletic groupings are considered problematic by many taxonomists, as it is not possible to talk precisely about their phylogenetic relationships, their characteristic traits and literal extinction. Related terms are stem group, chronospecies, budding cladogenesis, anagenesis, or 'grade' groupings. Paraphyletic groups are often relics from outdated hypotheses of phylogenic relationships from before the rise of cladistics.

Examples

Wasps are paraphyletic, consisting of the clade Apocrita without ants and bees, which are not usually considered to be wasps; the sawflies ("Symphyta") too are paraphyletic, as the Apocrita are nested inside the Symphytan clades.

The prokaryotes (single-celled life forms without cell nuclei) are a paraphyletic grouping, because they exclude the eukaryotes, a descendant group. Bacteria and Archaea are prokaryotes, but archaea and eukaryotes share a common ancestor that is not ancestral to the bacteria. The prokaryote/eukaryote distinction was proposed by Edouard Chatton in 1937 and was generally accepted after being adopted by Roger Stanier and C.B. van Niel in 1962. The botanical code (the ICBN, now the ICN) abandoned consideration of bacterial nomenclature in 1975; currently, prokaryotic nomenclature is regulated under the ICNB with a starting date of 1 January 1980 (in contrast to a 1753 start date under the ICBN/ICN).

Among plants, dicotyledons (in the traditional sense) are paraphyletic because the group excludes monocotyledons. "Dicotyledon" has not been used as a botanic classification for decades, but is allowed as a synonym of Magnoliopsida. Phylogenetic analysis indicates that the monocots are a development from a dicot ancestor. Excluding monocots from the dicots makes the latter a paraphyletic group.

Among animals, several familiar groups are not, in fact, clades. The order Artiodactyla (even-toed ungulates) as traditionally defined is paraphyletic because it excludes Cetaceans (whales, dolphins, etc.). Under the ranks of the ICZN Code, the two taxa are separate orders. Molecular studies, however, have shown that the Cetacea descend from artiodactyl ancestors, although the precise phylogeny within the order remains uncertain. Without the Cetaceans the Artiodactyls are paraphyletic. The class Reptilia is paraphyletic because it excludes birds (class Aves). Under a traditional classification, these two taxa are separate classes. However birds are sister taxon to a group of dinosaurs (part of Diapsida), both of which are "reptiles".

Osteichthyes, bony fish, are paraphyletic when circumscribed to include only Actinopterygii (ray-finned fish) and Sarcopterygii (lungfish, etc.), and to exclude tetrapods; more recently, Osteichthyes is treated as a clade, including the tetrapods.

The "wasps" are paraphyletic, consisting of the narrow-waisted Apocrita without the ants and bees. The sawflies (Symphyta) are similarly paraphyletic, forming all of the Hymenoptera except for the Apocrita, a clade deep within the sawfly tree. Crustaceans are not a clade because the Hexapoda (insects) are excluded. The modern clade that spans all of them is the Pancrustacea.

One of the goals of modern taxonomy over the past fifty years has been to eliminate paraphyletic taxa from formal classifications. Below is a partial list of obsolete taxa and informal groups that have been found to be paraphyletic.

Paraphyletic group	Excluded clades	Corresponding monophyletic taxon
Prokaryota	Eukaryota	Cellular organisms
Protista	Animalia, Plantae, Fungi	Eukaryota
Chromista	Archaeplastida, Provora	Diaphoretickes
Invertebrates	Vertebrata	Animalia
Platyzoa	Lophotrochozoa, Mesozoa	Spiralia
Fish	Tetrapoda	Vertebrata
Reptilia	Aves	Sauropsida
Lizards	Serpentes, Amphisbaenia	Squamata
Plagiaulacidans	Cimolodonta, Arginbaataridae	Multituberculata
Pelycosaurs	Therapsida	Synapsida
Even-toed ungulates	Cetacea	Artiodactyla
Archaeoceti	Neoceti	Cetacea
Prosimii	Simiiformes	Primates
Crustacea	Hexapoda	Pancrustacea
Wasps	Formicidae, Anthophila	Apocrita
Symphyta	Apocrita	Hymenoptera
Parasitica	Aculeata	Apocrita
Nautiloidea	Ammonoidea, Coleoidea	Cephalopoda
Charophyta	Embryophyta	Streptophyta
Dicotyledons	Monocotyledons	Angiospermae
Moths	Papilionoidea	Lepidoptera
Jellyfish	various hydrozoans	Medusozoa
Rotifera	Acanthocephala	Syndermata
Monkeys	Hominoidea	Simiiformes
Antelopes	Bovini, Caprini, Ovibovini	Bovidae

Paraphyly in species

Main article: Paraspecies

Species have a special status in systematics as being an observable feature of nature itself and as the basic unit of classification. Some articulations of the phylogenetic species concept require species to be monophyletic, but paraphyletic species are common in nature, to the extent that they do not have a single common ancestor. Indeed, for sexually reproducing taxa, no species has a "single common ancestor" organism. Paraphyly is common in speciation, whereby a mother species (a paraspecies) gives rise to a daughter species without itself becoming extinct. Research indicates as many as 20 percent of all animal species and between 20 and 50 percent of plant species are paraphyletic. Accounting for these facts, some taxonomists argue that paraphyly is a trait of nature that should be acknowledged at higher taxonomic levels.

Cladists advocate a phylogenetic species concept  that does not consider species to exhibit the properties of monophyly or paraphyly, concepts under that perspective which apply only to groups of species. They consider Zander's extension of the "paraphyletic species" argument to higher taxa to represent a category error.

Uses for paraphyletic groups

When the appearance of significant traits has led a subclade on an evolutionary path very divergent from that of a more inclusive clade, it often makes sense to study the paraphyletic group that remains without considering the larger clade. For example, the Neogene evolution of the Artiodactyla (even-toed ungulates, like deer, cows, pigs and hippopotamuses - Cervidae, Bovidae, Suidae and Hippopotamidae, the families that contain these various artiodactyls, are all monophyletic groups) has taken place in environments so different from that of the Cetacea (whales, dolphins, and porpoises) that the Artiodactyla are often studied in isolation even though the cetaceans are a descendant group. The prokaryote group is another example; it is paraphyletic because it is composed of two Domains (Eubacteria and Archaea) and excludes (the eukaryotes). It is very useful because it has a clearly defined and significant distinction (absence of a cell nucleus, a plesiomorphy) from its excluded descendants.

Also, some systematists recognize paraphyletic groups as being involved in evolutionary transitions, the development of the first tetrapods from their ancestors for example. Any name given to these hypothetical ancestors to distinguish them from tetrapods—"fish", for example—necessarily picks out a paraphyletic group, because the descendant tetrapods are not included. Other systematists consider reification of paraphyletic groups to obscure inferred patterns of evolutionary history.

The term "evolutionary grade" is sometimes used for paraphyletic groups. Moreover, the concepts of monophyly, paraphyly, and polyphyly have been used in deducing key genes for barcoding of diverse group of species.

Linguistics

Main article: Tree model

The concept of paraphyly has also been applied to historical linguistics, where the methods of cladistics have found some utility in comparing languages. For instance, the Formosan languages form a paraphyletic group of the Austronesian languages because they consist of the nine branches of the Austronesian family that are not Malayo-Polynesian and are restricted to the island of Taiwan.

Endling

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Endling

The last known thylacine (Tasmanian tiger), photographed at Hobart Zoo in 1933.

An endling is the last known individual of a species or subspecies. Once the endling dies, the species becomes extinct. The word was coined in correspondence in the scientific journal Nature.

Usage

The 4 April 1996 issue of Nature published a correspondence in which commentators suggested that a new word, endling, be adopted to denote the last individual of a species. The 23 May issue of Nature published several counter-suggestions, including ender, terminarch, and relict.

The word endling appeared on the walls of the National Museum of Australia in Tangled Destinies, a 2001 exhibition by Matt Kirchman and Scott Guerin, about the relationship between Australian peoples and their land. In the exhibition, the definition, as it appeared in Nature, was printed in large letters on the wall above two specimens of the extinct Tasmanian tiger: "Endling (n.) The last surviving individual of a species of animal or plant". A printed description of this exhibition offered a similar definition, omitting reference to plants: "An endling is the name given to an animal that is the last of its species."

In The Flight of the Emu: A Hundred Years of Australian Ornithology 1901-2001, author Libby Robin stated that "the very last individual of a species" is "what scientists refer to as an 'endling'".

In 2011, the word was used in the Earth Island Journal, in an essay by Eric Freedman entitled "Extinction Is Forever: A Quest for the Last Known Survivors". Freedman defined endling as "the last known specimen of her species."

In "The Sense of an Endling", author Helen Lewis describes the notion of an endling as poignant, and the word as "wonderfully Tolkien-esque".

Author Eric Freedman describes endling as "a word with finality", stating, "It is deep-to-the-bone chilling to know the exact date a species disappeared from Earth. It is even more ghastly to look upon the place where it happened and know that nobody knew or cared at the time what had transpired and why."

Notable endlings

Martha, the last passenger pigeon, died in the Cincinnati Zoo on September 1, 1914.

This is not a comprehensive list of contemporary extinction, but a list of high-profile, widely publicised examples of when the last individual of a species was known.

Birds

A dusky seaside sparrow (Ammospiza maritima nigrescens), officially declared extinct in 1990.

• The passenger pigeon (Ectopistes migratorius) became extinct at 1 p.m. on 1 September 1914 with the death of Martha, the last surviving member of the species, at the Cincinnati Zoo.
• Incas, the last known Carolina parakeet (Conuropsis carolinensis), died, also at the Cincinnati Zoo (and in the same cage as Martha), on 21 February 1918. He died within one year of his mate, Lady Jane. The species was officially declared extinct in 1939.
• Booming Ben, a solitary heath hen (Tympanuchus cupido cupido), was last seen 11 March 1932 on Martha's Vineyard, Massachusetts.
• Orange Band was the last known dusky seaside sparrow (Ammospiza maritima nigrescens), who died on 17 June 1987 at the Discovery Island zoological park at Walt Disney World Resort.
• The last known Kauaʻi ʻōʻō (Moho braccatus) was recorded singing a mating call on Kauai in 1987 by David Boynton. The bird is believed to have been killed by Hurricane Iniki in 1992, and the death of this individual also marked the extinction of the entire Mohoidae family.

Mammals

• In 1627, the last aurochs (Bos primigenius), an ancestor of bovine and cattle, died in a forest near what is now Jaktorów in modern-day Poland.

  

  A quagga mare at the London Zoo in 1870. This is the only specimen photographed alive.

• The quagga (Equus quagga quagga) became extinct in the wild in the late 1870s due to hunting for meat and skins, and the subspecies' endling died in captivity on 12 August 1883 at the Artis in Amsterdam.
• The final tarpan (Equus ferus ferus) died in captivity in the Russian Empire in 1903.
• On 7 September 1936, the last known captive thylacine (Thylacinus cynocephalus), also called Tasmanian tiger, died in Hobart Zoo, following persecution of the species through hunting and trapping. Information published about this individual has been conflicted throughout the decades following its death. An individual named Frank Darby invented the myth that it was named "Benjamin", and the claim was rapidly circulated by media and persists until today, even being repeated by Wikipedia itself. Other areas of contention include where it was captured and by whom, by whom it was captured, whether it was neglected in its zoo enclosure and even whether it was the last known surviving thylacine. Researchers Robert Paddle and Kathryn Medlock argue that the endling was female and died of neglect, while Gareth Linnard affirms that it was male (despite not being named Benjamin) and died of old age, citing its valued status in the zoo's collection. Regardless, the thylacine at Hobart Zoo is the last reputably-verified specimen of not only its species and genus, but also the entire family Thylacinidae. However, some individuals, such Barry Brooks and his colleagues, argue the thylacine probably persisted in the wild for several decades following the captive individual's death in 1936.
• The last known Mexican grizzly bear (Ursus arctos horribilis), also called oso plateado (silver bear) in Spanish, was shot in 1976 in Sonora, Mexico.

Taxidermised body of Celia, the final Pyrenean ibex

• Celia, the last Pyrenean ibex (Capra pyrenaica pyrenaica), was found crushed by a tree on 6 January 2000 in the Spanish Pyrenees, after hunting and competition from livestock reduced the population to one individual.
• The final Vietnamese Javan rhinoceros (Rhinoceros sondaicus annamiticus), was shot by a poacher at the Cát Tiên National Park in 2010, after habitat loss, poaching, and the Vietnam War reduced the population to one individual.

Reptiles and amphibians

Lonesome George, the last Pinta Island tortoise

• On 24 June 2012, Lonesome George, the last known Pinta Island tortoise (Chelonoidis niger abingdonii), died in his habitat in the Galápagos Islands.
• On 26 September 2016, Toughie, the last known Rabbs' fringe-limbed treefrog (Ecnomiohyla rabborum), died in the Atlanta Botanical Garden.

  

  'Toughie', the last known Rabb's fringe-limbed treefrog.

• After being considered possibly extinct for 113 years, a Fernandina Island Galápagos tortoise named Fernanda was found in 2019 for the Animal Planet series, Extinct or Alive. However, she is the only living individual known, making Fernanda an endling.

Invertebrates

• Turgi was the last Partula clarkei, a Polynesian tree snail, who died on 31 January 1996 in the London Zoo.
• A tank in the Bristol Zoo was the last refuge of Partula faba, a land snail from Ra'iātea in French Polynesia. The population dropped from 38 in 2012 to one in 2015. The last individual died on 21 February 2016.
• George was the last known individual of the Oahu tree snail species Achatinella apexfulva. He died on January 1, 2019, in captivity near Kailua, Hawaii.

Plants

The Curepipe Botanic Gardens in Mauritius have housed the last specimen of the palm Hyophorbe amaricaulis since the 1950s.

Only one living specimen of the tree species Madhuca diplostemon is known to exist.

Some seeds were found in an archaeological excavation in the Judean desert in 1986–87. In 2009, a specimen of an unknown species of Commiphora was successfully sprouted from one of these ancient seeds (dated 993 CE – 1202 calCE). The tree was named Sheba. In 2024, it was tentatively identified as tsori or Judean balsam, on the basis of taxonomy and resin properties matching ancient descriptions. Similar to Fernanda, Sheba is the only known individual of its species despite recent discovery or rediscovery.